Kaluza-Klein theory and Dirac equation in higher dimensional Riemann-Cartan space

The higher dimensional Kaluza-Klein theory in Riemann-Cartan space is discussed. To clarify its implications, we investigate the simplest five-dimensional case of the theory in detail. The Einstein-like, Maxwell, and Dirac equations in four-dimensional space-time are obtained by reducing the corresponding five-dimensional field equations. The effect of spin-spin interaction induced by torsion is revealed by analyzing the Dirac equation in this case.